JEE Mains · Physics · STD 12 - Electric potential and capacitance
- JEE Mains 2024
- Hard
- Numerical
Two identical charged spheres are suspended by string of equal lengths. The string make an angle of \(37^{\circ}\) with each other. When suspended in a liquid of density \(0.7 \mathrm{~g} / \mathrm{cm}^3\), the angle remains same. If density of material of the sphere is \(1.4 \mathrm{~g} / \mathrm{cm}^3\), the dielectric constant of the liquid is _______\(\left(\tan 37^{\circ}=\frac{3}{4}\right)\).
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(2\)
Step-by-step Solution
Detailed explanation
\(\text T \cos \theta=\mathrm{mg}\)
\(\mathrm{T} \sin \theta=\mathrm{F}_{\mathrm{e}}\)
\(\tan \theta=\frac{\mathrm{Fe}_{\mathrm{e}}}{\mathrm{mg}}\)
\(\tan \theta=\frac{F_e}{\rho_B V g}\) \(....(i)\)
\(\tan \theta=\frac{F_e}{\frac{k}{\left(\rho_B-\rho_{\mathrm{L}}\right) V g}}\) \(....(ii)\)
\(\text {From Eq. (i) (ii) }\)
\(\rho_{\mathrm{B}} \mathrm{Vg}=\left(\rho_{\mathrm{B}}-\rho_{\mathrm{L}}\right) \mathrm{kVg}\)
\(1.4=0.7 \mathrm{k}\)
\(\mathrm{k}=2\)
\(\mathrm{T} \sin \theta=\mathrm{F}_{\mathrm{e}}\)
\(\tan \theta=\frac{\mathrm{Fe}_{\mathrm{e}}}{\mathrm{mg}}\)
\(\tan \theta=\frac{F_e}{\rho_B V g}\) \(....(i)\)
\(\tan \theta=\frac{F_e}{\frac{k}{\left(\rho_B-\rho_{\mathrm{L}}\right) V g}}\) \(....(ii)\)
\(\text {From Eq. (i) (ii) }\)
\(\rho_{\mathrm{B}} \mathrm{Vg}=\left(\rho_{\mathrm{B}}-\rho_{\mathrm{L}}\right) \mathrm{kVg}\)
\(1.4=0.7 \mathrm{k}\)
\(\mathrm{k}=2\)
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